Rational Exponent, Radical Expressions and Equations Review

Front

What is a rational exponent?

Back

A rational exponent is an exponent that can be expressed as a fraction, where the numerator is a power and the denominator is a root. For example, x^(m/n) means the n-th root of x raised to the m-th power.

Front

How do you convert a radical expression to a rational exponent?

Back

To convert a radical expression to a rational exponent, rewrite the root as a fractional exponent. For example, √x can be written as x^(1/2) and ∛x as x^(1/3).

Front

What is the process for simplifying radical expressions?

Back

To simplify radical expressions, factor the radicand into perfect squares (or cubes, etc.), take the root of those factors, and simplify the expression.

Front

What is an extraneous solution?

Back

An extraneous solution is a solution that emerges from the process of solving an equation but does not satisfy the original equation.

Front

How do you check for extraneous solutions?

Back

To check for extraneous solutions, substitute the solution back into the original equation to see if it holds true.

Front

What is the relationship between rational exponents and roots?

Back

Rational exponents represent roots; for example, x^(1/n) represents the n-th root of x.

Front

How do you solve equations with rational exponents?

Back

To solve equations with rational exponents, isolate the variable and raise both sides of the equation to the reciprocal of the rational exponent.

Front

What is the simplified form of 8^(5/3)?

Back

The simplified form of 8^(5/3) is 32.

Front

What steps are involved in solving radical equations?

Back

To solve radical equations, isolate the radical, square both sides to eliminate the radical, and then solve the resulting equation.

Front

What is the importance of checking solutions in radical equations?

Back

Checking solutions in radical equations is important to ensure that the solutions are valid and not extraneous.